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package org.nd4j.linalg.api.ops;
import lombok.Data;
import org.nd4j.linalg.api.complex.IComplexNumber;
import org.nd4j.linalg.api.ndarray.INDArray;
import org.nd4j.linalg.factory.Nd4j;
import org.nd4j.linalg.util.ArrayUtil;
/**
* This implements a collapsing tad reduction
* based on different dimensions.
*
* The reason we need this is because of the fact that
* there are certain dimension combinations (usually > 1)
* that don't have an element wise stride.
*
* A way to bypass this problem is to expand the problem
* in to a 1 dimension reduction problem
* and then collapsing the results in to the equivalent
* shape of the multi dimension problem.
*
* An example problem would be an array of:
* linspace(1,24,24).reshape(2,2,3,2)
*
* The tad for reduction:
* 2,3 doesn't have an element wise stride.
*
* However, the tad for reduction:
* 3 does
*
* What we can exploit here is the ability
* to reshape problems of multiple dimensions
*
* in to equivalent expanded problems based on smaller tads
* eg:
* multiple reductions for each dimension along dimension 3
* followed by collapsing the problem in to an equivalent state
* as if we had specified 2,3 for the dimensions instead.
*
* This gives us a way of executing an element wise stride based
* algorithm that is executable on the gpu.
*
* For the GPU, we force each block to process a tad
* at the singular dimension level. Eg: dimension 3
*
* So for example along dimension 3 of the 2,2,3,2
* array we have 12 tensors along dimension.
*
* We then map those 12 tads to a reduction index.
*
* A reduction index is the equivalent value
* in teh result as if we had specified the reduction dimensions
* to be 2,3 instead.
*
* For example, if we have 12 tads for dimension 3
* we will only have 4 for dimensions 2,3
*
* The goal will be then to generate the equivalent results
* using dimension 3 but collapsing the results according to
* the dimension 2,3 space (remember: the reason we are doing this mapping
* is because we are trying to map the multi dimensional problem on to
* a problem that allows us to solve it via element wise stride)
*
*
* An example mapping relative to a gpu block is as follows:
* ([[[[ 1., 2.],
[ 3., 4.],
[ 5., 6.]],
[[ 7., 8.],
[ 9., 10.],
[ 11., 12.]]],
[[[ 13., 14.],
[ 15., 16.],
[ 17., 18.]],
[[ 19., 20.],
[ 21., 22.],
[ 23., 24.]]]])
* Along dimension 3 we will have tads of length 2
* and 4 reduction indexes we need to map for the
* 2,3 dimension problem.
*
*
* The first reduction index will map to the first 3 tads of length 2
* The next reduction index will map to the next 3, etc.
*
* We then process a reduction index per block on the gpu.
* If any gpu block index is > the number of
* reduction indexes we skip it.
*
* Note here we did this implementation because of
* race conditions on the block and shared memory.
*
* This way of mapping allows us to avoid race conditions.
*
*/
@Data
public class TadCollapseAccumulation extends BaseOp {
protected Op accum;
protected boolean performSmallerDimension;
protected int[] smallerDimension;
protected int[] originalDimension;
protected int tadsForSmallerDimension;
protected int tadsForLargerDimension;
public final static String DEFAULT_NAME = "collapseTad";
public TadCollapseAccumulation() {
}
/**
*
* @param accum the operation to accumulate
* @param originalDimension the bigger problem
* @param smallerDimension the smaller problem
*/
public TadCollapseAccumulation(Op accum, int[] originalDimension, int[] smallerDimension,boolean performSmallerDimension) {
this.accum = accum;
this.performSmallerDimension = performSmallerDimension;
this.originalDimension = originalDimension;
this.smallerDimension = smallerDimension;
tadsForSmallerDimension = accum.x().tensorssAlongDimension(smallerDimension);
tadsForLargerDimension = accum.x().tensorssAlongDimension(originalDimension);
}
/**
*
* @param accum the operation to accumulate
* @param originalDimension the bigger problem
* @param smallerDimension the smaller problem
*/
public TadCollapseAccumulation(Op accum, int[] originalDimension, int[] smallerDimension) {
this(accum, originalDimension, smallerDimension,true);
}
public TadCollapseAccumulation(Op accum, int[] originalDimension) {
this.accum = accum;
this.originalDimension = originalDimension;
}
public TadCollapseAccumulation(Op accum) {
this.accum = accum;
}
public TadCollapseAccumulation(INDArray x, Op accum) {
super(x);
this.accum = accum;
}
public TadCollapseAccumulation(INDArray x, INDArray y, INDArray z, long n, Op accum) {
super(x, y, z, n);
this.accum = accum;
}
public TadCollapseAccumulation(INDArray x, INDArray z, Op accum) {
super(x, z);
this.accum = accum;
}
public TadCollapseAccumulation(INDArray x, INDArray z, long n, Op accum) {
super(x, z, n);
this.accum = accum;
}
public Op getAccum() {
return accum;
}
@Override
public boolean isPassThrough() {
return true;
}
@Override
public void exec() {
//take the last dimension
if(smallerDimension == null) {
smallerDimension = new int[] {originalDimension[originalDimension.length - 1]};
}
if(accum instanceof Accumulation && performSmallerDimension) {
Accumulation acc2 = (Accumulation) accum;
//avoid the final transform till towards the end
acc2.setApplyFinalTransform(false);
Nd4j.getExecutioner().exec(acc2,smallerDimension);
}
else if(accum instanceof IndexAccumulation && performSmallerDimension) {
IndexAccumulation acc2 = (IndexAccumulation) accum;
Nd4j.getExecutioner().exec(acc2,smallerDimension);
}
/**
* Now combine the results based on
* the final dimension.
*/
INDArray aggregated = Nd4j.create(ArrayUtil.removeIndex(accum.x().shape(), originalDimension));
int smallerProblem = accum.x().tensorssAlongDimension(smallerDimension);
int biggerProblem = accum.x().tensorssAlongDimension(originalDimension);
if(accum instanceof Accumulation) {
int biggerTadLength = accum.x().tensorAlongDimension(0,originalDimension).length();
Accumulation accumulation = (Accumulation) accum;
for(int i = 0; i < smallerProblem; i++) {
int reductionIndex = reductionIndexForTad(i,biggerProblem,smallerProblem);
aggregated.putScalar(reductionIndex,accumulation.combineSubResults(aggregated.getDouble(reductionIndex),accumulation.z().getDouble(i)));
}
accum.setN(biggerTadLength);
accumulation.setApplyFinalTransform(true);
for(int i = 0; i < aggregated.length(); i++) {
aggregated.putScalar(i,accumulation.calculateFinalResult(aggregated.getDouble(i),biggerTadLength));
}
}
else if(accum instanceof IndexAccumulation) {
IndexAccumulation indexAccumulation = (IndexAccumulation) accum;
for(int i = 0; i < smallerProblem; i++) {
int reductionIndex = reductionIndexForTad(i,biggerProblem,smallerProblem);
aggregated.putScalar(reductionIndex,indexAccumulation.combineSubResults(accum.x().getDouble(i), i, aggregated.getDouble(reductionIndex), reductionIndex));
}
}
//set the new result
accum.setZ(aggregated);
}
@Override
public INDArray x() {
return accum.x();
}
@Override
public INDArray y() {
return accum.y();
}
@Override
public INDArray z() {
return accum.z();
}
@Override
public void exec(int... dimensions) {
this.originalDimension = dimensions;
exec();
}
@Override
public int opNum() {
return 0;
}
@Override
public String name() {
if(accum == null) {
return DEFAULT_NAME;
}
return accum.name();
}
@Override
public IComplexNumber op(IComplexNumber origin, double other) {
return accum.op(origin,other);
}
@Override
public IComplexNumber op(IComplexNumber origin, float other) {
return accum.op(origin,other);
}
@Override
public IComplexNumber op(IComplexNumber origin, IComplexNumber other) {
return accum.op(origin, other);
}
@Override
public float op(float origin, float other) {
return accum.op(origin, other);
}
@Override
public double op(double origin, double other) {
return accum.op(origin, other);
}
@Override
public double op(double origin) {
return accum.op(origin);
}
@Override
public float op(float origin) {
return accum.op(origin);
}
@Override
public IComplexNumber op(IComplexNumber origin) {
return accum.op(origin);
}
@Override
public Op opForDimension(int index, int dimension) {
return accum.opForDimension(index, dimension);
}
@Override
public Op opForDimension(int index, int... dimension) {
return accum.opForDimension(index,dimension);
}
/**
* Given an linear index, element wise stride
* and the length of each tad
* map a linear index to a tad
* @param i the index to map
* @param elementWiseStride the element wise stride for the tads
* @param numElementsPerTad the number of elements
* per tad
*/
public static int tadIndex(int i,int elementWiseStride,int numElementsPerTad) {
return i / (numElementsPerTad * elementWiseStride);
}
/**
* Map a tad to a
* reduction index.
* @param tadIndexForOriginal the original tad index for the
* split up problem (eg: split is dimension 3 mapping to a 2,3 problem)
* @param tadsForReduced the number of tads for the shrunk down problem (eg: 2,3)
* @param tadsForOriginal the number of tads for the smaller problem (eg: 3)
*/
public static int reductionIndexForTad(int tadIndexForOriginal,int tadsForReduced,int tadsForOriginal) {
if(tadIndexForOriginal == 0)
return 0;
return tadIndexForOriginal / (tadsForOriginal / tadsForReduced);
}
/**
* Computes the number of tads
* per reduce index for the
* reduction tad.
*/
public static int tadsPerReduceIndex(int tadsForReduce,int tadsForOriginal) {
return tadsForOriginal / tadsForReduce;
}
/**
* Maps a linear index to a reduction index
* @param i the linear index to map
* @param elementWiseStride the element wise stride
* for the multiple problem
* @param tadNum the number of tads for the shrunken problem
* @param originalTadNum the tad number for the reduced version of the problem
*/
public static int reductionIndexForLinear(
int i
,int elementWiseStride
,int numElementsPerTad
,int tadNum
,int originalTadNum) {
int tad = tadIndex(i,elementWiseStride,numElementsPerTad);
return reductionIndexForTad(tad,tadNum,originalTadNum);
}
}
